an unpublished letter from henry oldenburg to johann heinrich rahn

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254 Noel Malcolm
A long list of mathematical books now followed (accompanied in some cases by
Collins’s comments on them), including works by Kinckhuysen, Ferguson, Wilkens,
Smyters, van der Huyps, Bartholinus, de Sluse, Rinaldini, Fermat, de Billy, Barrow, Dary
and Wallis. In the next section of the draft, headed ‘As to Opticall affaires’, Collins added
details of works by Manzini, Eschinardi, de Gottignies, Cherubin, Barrow and
Bartholinus; he then reproduced some long extracts from a recently published work by
Johann Heinrich Ott, describing a new method, invented by Ott, of making hyperbolic
lenses. In a final section he gave details of a number of recent or forthcoming publications
in Italy, France, and Spain, introducing them with the comment ‘Concerning bookes
mathematicall we heare of divers lately published in Italy &c. but have seen none of
them, however thinke fit to give you ane account of them, that we may receive your opinion
concerning such as you have seen, and be somewhat informed of what argument they
treat’: in this list he included works by Rosetti, Castelli, Baliani, Borelli, Mengoli,
Blondel, Milliet de Chales, de Gottignies, Mouton and de la Loubère. 16 With only a handful
of exceptions (among them, two treatises by Borelli, a work on geodesy by Jean
Picard and a mathematical treatise by John Kersey), the list of books given here by
Collins was incorporated by Oldenburg in his letter to Rahn; Ott’s work was mentioned
there, though the lengthy extracts were not in the end included.
Collins’s list of recent publications also referred, somewhat casually, to the translation
of Rahn’s own Teutsche Algebra: ‘In England about 4 yeares since the Introduction written
by himselfe was translated and printed with divers alterations therein made by D r
Pell.’ 17 But this comment, and the initial remark about Rahn’s reduction of the
Diophantine problems into ‘the style of the learned D r Pell’, were not the only references
to Pell in Collins’s draft. Collins had in fact enjoyed very close relations with Pell; not
only had he assisted with the preparation of the modified translation of Rahn’s book
(dealing with the printer in London while Pell was absent from the capital), but when Pell
returned to London in the late summer of 1669 he became a lodger in Collins’s house. 18
Collins was especially keen to learn about the advanced algebraic techniques which Pell
had developed, but which he had not made public; indeed, this desire might have been
the underlying reason for inviting Pell into his home. But it seems that Pell was reluctant
to have his secrets wormed out of him, and Collins’s letters to other mathematicians during
this period are a constant litany of complaints about Pell’s failure to impart any of his
important discoveries to him. 19 Unable to learn the details of Pell’s methods, Collins
adopted a strategy of circulating to other mathematicians descriptions of the feats Pell
claimed to be able to perform, with such hints as he could gather of how he performed
them, in the hope that they could work out the missing steps in the argument. 20 So it was
entirely in keeping with Collins’s own epistolary strategy that his draft reply to Rahn
included another such request. Indeed, making this request—specifying the most useful
quid pro quo with which Rahn might respond to this deluge of bibliographical information—might
well have been the most important function of the letter in Collins’s eyes:
That which we chiefly here desire, is that some easy method might be found and communicated
for obtaining the rootes of the higher sort of Aequations by logarithmes, and having some kinde
of intelligence that D r Pell hath attained something extraordinary in that kinde, but hath not as yet
evulged the same though very desirable, we thought fit to impart to you the Sence of a Member
of the Society about that affaire, and earnestly covet your observations thereupon. 21